The FQHE occurs when charge carriers like electrons are confined to a 2D plane, as in graphene, and are subjected to a perpendicular magnetic field in the Z-direction. If a current flows in the X-direction, a voltage – the Hall voltage – occurs in the Y-direction. At very low temperatures, this voltage is quantized in distinct steps or Hall states.

Fractional charges

The FQHE is different from the better-known integer quantum Hall effect and is a result of strong interactions between electrons that occur in some materials. These interactions make the charge carriers in a FQHE material behave as quasiparticles with charge that is a fraction of that of an electron. These fractionally charged quasiparticles obey so-called fractional statistics, a feature that may be important for developing future quantum computers. In addition to the FQHE, these strong interactions often lead to important collective phenomena such as superconductivity, magnetism and superfluidity. Therefore understanding strong interactions is of fundamental importance in condensed-matter physics.

Graphene is a layer of crystalline carbon just one atom thick and is different from other materials in that its charge-carrying electrons whiz around at extremely high speeds, behaving like relativistic particles with no rest mass. Researchers have already shown that the relativistic charge carriers in graphene interact strongly with each other and that this phenomenon can be detected as the FQHE.

Unconventional sequence

Now, Amir Yacoby and colleagues at Harvard University and the Max-Planck Institute for Solid State Physics have shown that the FQHE in graphene is different to that in other materials. "We found an unconventional sequence of [fractional quantum hall] states in graphene, which are a consequence of the underlying symmetries in the material," explained Yacoby. "These states provide insights into the interplay between these symmetries and electron–electron interactions in graphene."

The researchers obtained their results by using a scanning single-electron transistor (SET) to probe samples of suspended graphene that were subject to an applied magnetic field. The SET is a special type of local probe that is particularly non-invasive, said team member Ben Feldman. It measures the presence of energy gaps in the electronic spectrum of materials with a sensitivity that no other technique can match and is therefore ideal for exploring phenomena like the FQHE.

"One other important finding of our research is that small regions of very clean graphene exist, even when macroscopic samples are relatively dirty," he told "Studying graphene with local probes like ours may thus yield further interesting insights into graphene."

Studying electron–electron interactions

The experiments also back up the previous research, which showed that electrons in graphene interact strongly and that the resulting physics is very different to that observed in more conventional systems. "Graphene is therefore a promising material for studying electron–electron interactions," said Yacoby.

The team now plans to continue exploring the unusual FQHE in graphene. "We would especially like to better understand how the electrons are ordered in the various FQH states," he added. "We are also interested in learning about the FQHE in related materials like bilayer graphene."

The present work is detailed in Science.